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Loop gravity in terms of spinors

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Published under licence by IOP Publishing Ltd
, , Citation Etera Livine and Johannes Tambornino 2012 J. Phys.: Conf. Ser. 360 012023 DOI 10.1088/1742-6596/360/1/012023

1742-6596/360/1/012023

Abstract

We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and discrete geometries. This results in a new, unitarily equivalent formulation of the theory on a generalized Bargmann space. Since integrals over the group are exchanged for straightforward integrals over the complex plane we expect this formalism to be useful to efficiently organize practical calculations.

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10.1088/1742-6596/360/1/012023